diff --git a/src/net.rs b/src/net.rs
index 132cbff90..63516264f 100644
--- a/src/net.rs
+++ b/src/net.rs
@@ -152,13 +152,15 @@ where
 
     // Start additional connection attempts after 300 ms, 1 s, 5 s and 10 s.
     // This way we can have up to 5 parallel connection attempts at the same time.
-    let mut delays = [
+    let mut delay_set = JoinSet::new();
+    for delay in [
         Duration::from_millis(300),
         Duration::from_secs(1),
         Duration::from_secs(5),
         Duration::from_secs(10),
-    ]
-    .into_iter();
+    ] {
+        delay_set.spawn(tokio::time::sleep(delay));
+    }
 
     let mut first_error = None;
 
@@ -167,37 +169,42 @@ where
             connection_attempt_set.spawn(fut);
         }
 
-        let one_year = Duration::from_secs(60 * 60 * 24 * 365);
-        let delay = delays.next().unwrap_or(one_year); // one year can be treated as infinitely long here
-        let Ok(res) = timeout(delay, connection_attempt_set.join_next()).await else {
-            // The delay for starting the next connection attempt has expired.
-            // `continue` the loop to push the next connection into connection_attempt_set.
-            continue;
-        };
+        tokio::select! {
+            biased;
 
-        match res {
-            Some(res) => {
-                match res.context("Failed to join task") {
-                    Ok(Ok(conn)) => {
-                        // Successfully connected.
-                        break Ok(conn);
+            res = connection_attempt_set.join_next() => {
+                match res {
+                    Some(res) => {
+                        match res.context("Failed to join task") {
+                            Ok(Ok(conn)) => {
+                                // Successfully connected.
+                                break Ok(conn);
+                            }
+                            Ok(Err(err)) => {
+                                // Some connection attempt failed.
+                                first_error.get_or_insert(err);
+                            }
+                            Err(err) => {
+                                break Err(err);
+                            }
+                        }
                     }
-                    Ok(Err(err)) => {
-                        // Some connection attempt failed.
-                        first_error.get_or_insert(err);
-                    }
-                    Err(err) => {
-                        break Err(err);
+                    None => {
+                        // Out of connection attempts.
+                        //
+                        // Break out of the loop and return error.
+                        break Err(
+                            first_error.unwrap_or_else(|| format_err!("No connection attempts were made"))
+                        );
                     }
                 }
-            }
-            None => {
-                // Out of connection attempts.
+            },
+
+            _ = delay_set.join_next(), if !delay_set.is_empty() => {
+                // Delay expired.
                 //
-                // Break out of the loop and return error.
-                break Err(
-                    first_error.unwrap_or_else(|| format_err!("No connection attempts were made"))
-                );
+                // Don't do anything other than pushing
+                // another connection attempt into `connection_attempt_set`.
             }
         }
     };
@@ -205,6 +212,11 @@ where
     // Abort remaining connection attempts and free resources
     // such as OS sockets and `Context` references
     // held by connection attempt tasks.
+    //
+    // `delay_set` contains just `sleep` tasks
+    // so no need to await futures there,
+    // it is enough that futures are aborted
+    // when the set is dropped.
     connection_attempt_set.shutdown().await;
 
     res